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Question 67

Consider the following statements:
$$P$$: I have fever
$$Q$$: I will not take medicine
$$R$$: I will take rest
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

$$P$$: I have fever, $$Q$$: I will not take medicine, $$R$$: I will take rest.

"If I have fever, then I will take medicine and I will take rest."

"I will take medicine" = $$\sim Q$$ (negation of "I will not take medicine").

So the statement is: $$P \to (\sim Q \wedge R)$$.

$$\equiv \sim P \vee (\sim Q \wedge R)$$

$$\equiv (\sim P \vee \sim Q) \wedge (\sim P \vee R)$$

This matches option 1: $$((\neg P) \vee \neg Q) \wedge ((\neg P) \vee R)$$.

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